# math

The distance between towns M and N is 280 km. A car and a lorry travel from M to N.
The average speed of the lorry is 20 km/h less than that of the car. The lorry takes 1 h 10 min more than the car to travel from M and N.
(a) If the speed of the lorry is x km/h, find x
(b) The lorry left town M at 8: 15 a.m. The car left town M later and overtook the lorry at 12.15 p.m. Calculate the time the car left town M.

1. 👍
2. 👎
3. 👁
1. speed of lorry ---- x km/h
speed of car ----- x+20 km/h

time for the car = 280/(x+20)
time for lorry = 280/x

280/x - 280/(x+20) = 70/60
divide by 70
4/x - 4/(x+20) = 1/60
times 60x(x+20), the LCD
240(x+20) - 240x = x(x+20)
240x + 4800 - 240x = x^2 + 20x
x^2 + 20x - 4800 = 0
(x - 60)(x + 80) = 0
x = 60 or x is a negative

the speed of the lorry is 60 km/h

b) at the time of overtaking, the lorry had gone for
4 hrs, thus it had gone 240 km
for the car to go those same 240 km would have taken 240/80 hrs or 3 hrs.
So just "backup" 3 hrs from 12:15

1. 👍
2. 👎

## Similar Questions

1. ### Math

An object's velocity after t seconds is v(t)= 38-2t feet per second. a. How many seconds does it take for the object to come to a stop (velocity = 0)? b. How far does the car travel during that time? c. How many seconds does it

2. ### Maths

The scale on a map is 1 :500000, Two towns ate 7cm apart, whats the actual distance between towns. Give your answers in Km.

3. ### Trigonometry

A passenger in an airplane flying at an altitude of 10 kilometers sees two towns directly to the left of the plane. The angles of depression to the towns are 28° and 55°. How far apart are the towns?

4. ### Math

A matatu left town k at 7.00am and travelled towards town M at an average speed of 60km/hr.A car left town M at 9.00am and travelled towards K at an average speed of 80km/hr. The distance between the two towns is 324km.A:find the

1. ### math

The stopping distance d of a car after the brakes have been applied varies directly as the square of the speed r. If a car traveling 40 mph can stop in 100 ​ft, how fast can a car travel and still stop in 256 ​ft?

2. ### Math

A car traveled at a constant speed for 4 hours and covered 144.6 miles. It used 12 gallons of gas to travel this distance. How far did the car go in 1 hour? How far did the car travel on 1 gallon of gas?

3. ### Mathematics

Two cars drive from town A to town B at constant speeds. The blue car travels 25 miles per hour and the red car travels 60 miles per hour. The blue car leaves at 9:30 am and the red car leaves at noon. The distance between the two

4. ### mechanics-physics

A lorry of mass 1000kg moving initially at 10m/s increases to 25m/s. In 5sec the on the lorry is 15,000Newtons; calculate: (a) Acceleration (b) The distance covered

1. ### maths

the scale factor on a map is 1 : 500 000 2 towns are 8cm apart on the map. work out the actual distance between the 2 towns. give your answer in kilometres.

2. ### Math (unit rates)

A car traveled on the highway at 65 miles per hour for 45 minutes. What distance did the car travel?

3. ### MATH

A MAP HAS THE SCALE OF 1 INCH = 80 MILES. WHAT IS THE ACTUAL DISTANCE , IN MILES, BETWEEN TWO TOWNS THAT ARE 4 1/2 INCHES APART ON THE MAP? 1. 280 2. 320 3. 324 4. 360 5. 400

4. ### Physics

A race car can be slowed with a constant acceleration of -11 m/s^2 a. If the car is going 55 m/s, how many meters will it travel before it stops? b. How many meters will it take to stop a car going twice as fast? According to one